The purpose of this project is to develop theory for the interpretation of biomedical and chemical measurement techniques. At present we have worked on two such techniques: single-molecule spectroscopy (SMS) and optical spectroscopy applied to estimate optical tissue parameters to distinguish between normal and abnormal tissues. In the past year we have concluded our development of the theory of SMS applied to two-state randomly interconverting systems, showing that our techniques can also be applied to analyze systems where correlations due to noise are essentially equal to zero, which rules out analysis methods based on the existence of correlations. The second project deals with the theory of optical measurements as used to estimate optical properties of human tissue. This project has generated research on defining the region of tissue visited by laser-generated photons. Since it has been shown that properties of tissue can successfully be found from models based on random walks on discrete lattices, we have identified the region visited by photons with the expected number of distinct sites visited by the random walk conditioned to emerge at an interface, where it can be identified with a light intensity. A physical model has been developed for this process and applied to reflectance and transillumination measurements. In the past year we have continued our work on the theory of single molecule fluorescence spectroscopy by finding an expression for the joint probability-probability density for the time spent in the fluorescent state and the number of sojourns in that state. If the available data is good enough it permits a more precise estimation of rate constants for the underlying system. With regard to the use of optical techniques for imaging purposes we have proposed a technique for characterizing the region probed by a photon which is ultimately re-emitted by the medium (i.e., tissue). This is based on the observation that tissue can be modeled as a simple cubic lattice. It is possible to calculate the expected number of lattice sites visited by a re-emitted photon. This then provides a parameter related to the region visited by the photon.